46 Wm. A. Notion on the Variations 



If we denote the temperature of the earth, in Centigrade degrees, 

 by T, we shall have for the velocity of cooling of the earth, by 

 radiation into space, 



V=2-037((1-0077) T - (T ^ 7 -y r4T ) =2-03r((l-0077) T --339 



According to this formula the velocity of cooling of the earth's 

 surface at 0° C, (32° F.,) is to the velocity of cooling at 15° C, 

 (59° F.) as 67 to 78 — that is, the rate of cooling diminishes, from 

 59° F. to 32° F., 4 of its amount at 59°. 



Formula (1) was obtained by a comparison of theory with the 

 experiments of Petit and Dulong. It may well happen that 

 when we come to apply it to a case in which the temperature of 

 the medium exterior to the cooling body is far below the range of 

 the experiments, it will not give exact results. 



In the application of this formula, I have supposed the radiation 

 of the earth to be directly into free space. As a matter of fact, 

 it is through the atmosphere, and therefore the rate of cooling of 

 the earth must depend upon the mean temperature and also the 

 absorptive action of the atmosphere. To apply formula (1) to 

 the case of the earth, d should therefore be taken equal to the tem- 

 perature of the sky, instead of the temperature of space : or, we 

 may introduce into the formula another subtractive term, repre- 

 senting the emissive power or absolute radiation of the atmos- 

 phere. We must also allow for the absorption of heat by the 



atmosphere. Pouillet estimates this at a little less than ^. Sup- 



2 



1 . . . 1 



posing it to be ~, and also that - of the heat radiated downward 



from the air reaches the surface of the earth, and denoting by t 

 the mean temperature of the air, we have 



V =ma 



t 



?Y ma rna 



~~2 vT 



(3.) 



It appears from the observations made by Pouillet with the ac- 

 tinometer, that the mean temperature of the atmosphere is about 

 35° C. below the temperature of the air, and falls, during the 

 night, at about the same rate as the temperature at the earth's 

 surface. Taking this result, and making the calculations for 

 ra = l, we find the velocities of cooling at 32° F. and 59° F. to 

 be to each other as 77 to 86, or that the diminution is a little 

 more than T ' fi of the velocity of cooling at 59° F. According to 

 Pouillet, the absorptive power of the entire atmosphere for terres- 

 trial heat is greater than 0*8, but as the heat radiated downwards 

 from the atmosphere passes only through a portion of it, the value 



of - is doubtless less than 0-8. It is to be taken into account 

 n 



